A piece of wood has dimensions 'a', 'b' and 'c'. Its relative density is d. It is floating in water such that the side 'a' is vertical. It is now pushed down gently and relesed. The time-period of S.H.M. is

Options

A. `(1)/(2pi) sqrt((g rho)/(ld))`
B. `(1)/(2pi) sqrt((g rho)/(bd))`
C. `(1)/(2pi) sqrt((g rho)/(hd))`
D. `(1)/(2pi) sqrt((g d)/(h rho))`

Answer

D

Explanation

When the wooden block is pushed down through x, the volume of the liquid displaced = l bx
Restoring force, F = Mass of the liquid displaced `F = (l b x rho) g`
`ma = l b x rho g`
`a = (lbx rho)/(m)g = (lbx rho)/(lbhd) g`
`a = ((lb rho x)/(lbhd))g`
`omega^(2) = (g rho)/(hd), f = (1)/(2pi) sqrt((g rho)/(hd))`